1. Field
This patent specification relates to electromagnetic measurements made in connection with boreholes. More particularly, this patent specification relates to methods and systems for correcting for or determining attenuation due to a conductive casing of a borehole while making electromagnetic measurements.
2. Background
Electromagnetic (EM) induction surveys are used to map the electrical conductivity of geologic formations between boreholes and radially away from a single well. The latter, usually referred to as induction logging, has been in routine use for over fifty years. These surveys are performed in open holes, that is, holes that have not been lined with a conductive casing such as a metallic casing.
Recently, the concepts of induction logging have been extended to surveys between uncased wells and between wells which have conducting metallic liners. There is also interest in the use of logging between surface and downhole sensors and within single wells that are cased with metallic liners. The metallic liners (casing) introduce several problems for EM induction surveys. The first is that the signal from the transmitter to the receiver is severely attenuated in passing through the metallic casing because of its high conductivity and, usually, high magnetic permeability. The second is that the conductivity, permeability and thickness are variable along the length of the casing. A third problem is that the transmitters in these surveys are normally multi-turn solenoids that have a core of high magnetic permeability. At high current levels in the solenoid the permeability of the core material, and of the surrounding casing itself, is driven into a nonlinear regime. Under these circumstances the current in the solenoid is not proportional to the net radiated field. Receivers are also high-mu (high-μ) cored solenoids but generally are not operated at high field levels where non linear effects are seen.
Induction surveys typically share the same physical principles. A transmitter, usually a multi-turn coil of wire, carries an alternating current of frequency ω (radians/sec) when placed in a wellbore. The current in the coil creates a time varying magnetic field in the surrounding subterranean formation which in turn, by Faraday's law, induces an electromotive force (emf). The emf drives currents in the formation, which are proportional to the formation conductivity. Finally a receiver is positioned either in the same wellbore as the transmitter or in another wellbore separated from the wellbore containing the transmitter. The receiver measures the magnetic field arising from the transmitter and the secondary, or induced, currents in the formation.
Conventional induction logging uses a combination of multiple receivers and/or multiple transmitters connected in series so as to cancel the mutual signal in air. In general, a theoretical model for such a system embedded in a formation of arbitrary resistivity is then used to match or interpret the received fields. In some applications, the absolute value of the average formation resistivity is not as important as the ability to map variations of resistivity within the formation. To determine this spatial variation of formation resistivity the surveys typically involve placing the transmitter at multiple positions (e.g. depths) in the wellbore and measuring the resulting field at multiple receiver positions for each transmitter position. In crosshole surveys, such a survey yields a data set similar to the methods of tomography.
There is a range of frequencies in which such induction surveys are practical. Below a certain frequency the secondary fields from the formation are simply too small to be detected with practical receivers and above a certain frequency the casing attenuation obliterates the formation response. The frequency range depends on the type of casing used. Carbon steel casing in general has a conductivity (σ) of 5e6 S/m, permeability (μ) of 100, while Chromium casing is essentially non-magnetic (μ=1), and has a conductivity (σ) of 1e6 S/m. As a result, Chromium casing is more favorable for induction surveys because Chromium attenuates the EM signal much less than the carbon steel casing at the same frequency. Thus, for practical field systems and depending on the conditions, in Chromium cased boreholes the range of practical frequencies may include up to several hundred Hz, while in carbon steel cased boreholes, the frequency may be limited to roughly 100 Hz. See e.g. G. Gao, D. Alumbaugh, P. Zhang, H. Zhang, C. Levesque, R. Rosthal, J. Liu, A. Abubakar, and T. Habashy, “Practical implications of nonlinear inversion for cross-well electromagnetic data collected in cased-wells,” SEG extended abstract, 2008, hereinafter referred to as “G. Gao, 2008” and which is hereby incorporated by reference herein.
A problem is that within the frequency range described above, the casing properties (conductivity (σ), permeability (μ, for Chromium casing μ is roughly 1), thickness (t) and inner radius (r)) are not constant along the length of casing. Since the casing attenuation is so strong, small variations in its properties produce variations in the fields seen by a receiver that are large compared to the variations expected from desired formation variations. A further problem is that the strength of the transmitter, known as the transmitter moment, must be known so that moment variations are not misinterpreted as variations in the formation conductivity.
It is therefore highly desirable to provide a means to eliminate, or correct for, these casing variations. As shown in G. Gao, 2008, removing the casing effects from the measurements posts significant benefits on the image quality of the EM inversion/imaging. Consider the schematic for a crosswell survey shown in FIG. 1a. Boreholes 110 and 112 are shown in formation 100. Both boreholes are cased with a conductive liner such as high-carbon steel. The transmitter Ti, reference number 120, at location i in borehole 110, produces at field Bij at receiver 122 at location j of borehole 112. The field Bij can be expressed as the product of:Bij=MigijKijfkjki=GijKijkjki  (1)where the moment (or strength), Mi of the transmitter 120 and a purely geometric term, gij, are combined here into Gij; the desired formation response, the response of the induced currents, if no casing was present; Kfij, is the casing attenuation at the transmitter ki; and the casing attenuation at the receiver 124 at location j of borehole 112, kj.
Augustin, A. M., Kennedy, W. D., Morrison, H. F., and Lee, K. H., A theoretical study of surface to borehole electromagnetic logging in cased holes: Geophysics, 54, 90-99 (1989), hereafter referred to as “Augustin et al (1989),” and incorporated by reference herein, shows that the casing attenuation terms ki and kj are multiplicative for simple transmitters and receivers operating in homogeneous casing.
One known solution to the casing attenuation problem is to use ratios of received fields to eliminate ki and kj. As an illustrative example of this method, suppose the receiver borehole is not cased so that kj is one. Now for a fixed position of the transmitter, we can take the ratio of fields at two different receiver positions A & B
                                                        B              ij                        ⁡                          (              A              )                                                          B              ij                        ⁡                          (              B              )                                      =                                                            G                ij                            ⁡                              (                A                )                                      ⁢                                          K                ij                f                            ⁡                              (                A                )                                      ⁢                          k              i                                                                          G                ij                            ⁡                              (                B                )                                      ⁢                                          K                ij                f                            ⁡                              (                B                )                                      ⁢                          k              i                                                          (        2        )            and the casing attenuation ki cancels out. The Gij's are known so the full ratio yields a formation response ratio that is casing independent. Such response ratios can be fitted to models of the formation just as are the responses themselves. Commonly owned U.S. Pat. No. 6,294,917, herein after “the '917 patent” and incorporated by reference herein, describes how the ratio method can easily be extended to double ratios if both boreholes are cased.
As shown in G. Gao 2008: (1) the ratios described above are relatively sensitive to noise in the measured fields; and (2) in the modeling, or inversion, process the use of ratio data reduces the sensitivity of the method to variation in formation resistivity near the boreholes. In the example shown in FIG. 1a, this area of reduced sensitivity would occur near the transmitter borehole 110.
An alternative solution to the ratio approach is described in WO 2009/002763A1 (US 20090005993). The alternative solution, referred to herein as the “inversion” method reduces the effects of noise by inverting the casing attenuation factors and formation property simultaneously. However, as shown in G. Gao 2008, the inversion method approach also reduces the sensitivity to variation in formation resistivity near the boreholes, which reduces the resolution of the resistivity/conductivity image obtained by EM inversion/imaging.
Still another known solution, at least for the cross-borehole mode of operation, is to place an auxiliary receiver adjacent to the transmitter (or auxiliary transmitter adjacent to the receiver). This method is described in commonly owned U.S. Pat. No. 7,030,617, hereinafter referred to as “the '617 patent,” and incorporated by reference herein.
Consider FIG. 1b for the case where the object is to solve for the casing correction for the transmitter 120 in cased borehole 110 when a receiver Rj, 122, is in an open-hole borehole 114.
The field Bk at an auxiliary receiver Rk, 130, is effectively governed by the equation:Bik=Gikkikk  (3)because the spacing between the transmitter 120 and auxiliary receiver 130 is too small for there to be any meaningful formation response.
The field at the distant receiver 122 is governed by the equation:Bij=GijKijfki  (4)
If the auxiliary receiver, Rk, 130 is sufficiently far from the transmitter 120 and if each has the same coupling to the casing of borehole 110 (same length of solenoid, same core and winding configuration) and if the casing is uniform along its length, then ki=kk and so:
                                          B            ik                    =                                    G              ik                        ⁢                          k              i              2                                      ⁢                                  ⁢        or                            (        5        )                                          k          i                =                                            B              ik                                      G              ik                                                          (        6        )            Then
      B    ij    =            G      ij        ⁢                  K        ij        f            ·                                    B            k                                G            ik                              and this is easily solved for the desired formation response Kfij.
If, however the transmitter 120 is too close to the receiver 122 so that separability is no longer the case; (2) if the variations in casing properties occur on a scale small relative to the spacing of the transmitter 120 and auxiliary receiver 130; (3) in some cases where it is impractical to make the auxiliary receiver 130 electrically equivalent to the transmitter; or (4) if the transmitter 130 is operating in a non-linear region, the results from the method of the '617 will be less accurate compared to other methods.
Another method combining auxiliary receiver-transmitters with the ratio method has been described in U.S. Patent Application Publication No. 2009/0091328 (U.S. patent application Ser. No. 11/868,379, filed on Oct. 5, 2007), hereinafter “the '379 application,” and incorporated by reference herein. The method described in the '379 application uses an auxiliary transmitter and receiver as shown in FIG. 2. In this case the receiver 222, Rj can also be used as a transmitter to the receiver at location k. The field at Rj from the main transmitter 220, Ti at location i, is given byBij=Gijkikj  (7)and the field at receiver 224 at location k, Bik is given byBik=Gikkikk  (8)
The field at location k due to transmitter/receiver 222 at j is given byBjk=Gjkkjkk  (9)
Since all the Bs and Gs are known, there are three equations in three unknowns: ki, kj and kk. It is possible to solve for ki since the field at the distant site (shown as a coil 230 at location A), is given by:BiA=GiAkiAfKi  (10)
With ki known, the required KiAf can also be determined.
The latter multiple auxiliary system is straight-forward in concept but is relatively complicated to implement in a practical system because the instrument actually lowered into the borehole 210 is long and heavy. The latter multiple auxiliary system does have the advantage that nonlinear effects at the transmitter are included in ki.
Thus it is desirable to use measurements on the solenoid itself to predict the casing attenuation factor at the solenoid. One recent development is described in commonly owned U.S. Pat. No. 8,326,539 (U.S. patent application Ser. No. 12/117,089, filed May 8, 2008) hereinafter referred to as “the '089 application,” and incorporated herein by reference. The '089 application describes the use of measurements of the impedance of the transmitting or receiving coil to determine the casing attenuation factor of the casing around the coil. The casing parameters (conductivity, magnetic permeability, and casing thickness) and the casing attenuation factors can be determined from the impedance measurements of at least two frequencies (from a pre-calculated table), then the determined casing parameters can be used to calculate the casing attenuation factors. Alternatively, a table between the impedance and casing attenuation factors can be directly established. However, the '089 application does not include any approach for determining the casing parameters such as conductivity, magnetic permeability, and casing thickness from the impedance measurements. It is well known that the casing parameters are typically coupled together in a complicated way and the coupling varies significantly with the casing parameters and the frequency, which makes it challenging to separately determine the casing parameters without additional constraints.
Thus it is desirable to provide a more robust method of using measurements on a solenoid to predict the casing attenuation factor as well as other casing parameters at the location of the solenoid.